Exact Solutions of Bianchi Types $I$ and $V$ Spacetimes in $f(R)$ Theory of Gravity

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

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16 pages, accepted for publication in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/26/23/235020

In this paper, the crucial phenomenon of the expansion of the universe has been discussed. For this purpose, we study the vacuum solutions of Bianchi types $I$ and $V$ spacetimes in the framework of $f(R)$ gravity. In particular, we find two exact solutions in each case by using the variation law of Hubble parameter. These solutions correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models is discussed. Moreover, the function of the Ricci scalar is evaluated for both the models in each case.

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